It's a pretty bridge, nothing really special about it. The best view is from a waterboat, actually. It doesn't have fancy colors or anything and during the day it appears a seemingly innocent bridge.
Night, pretty. Day, pass it up. If you happen to be passing it by, then have a look, but honestly don't go out of your way to see the bridge itself; though it leads to some interesting places like Odaiba.
With respect to the other reviewers, I find the best place to view this bridge is from the deck of the booze cruise leaving from Hammamatsucho. Other that how it looks from the deck of a boat...what can you say...it's a bridge. It goes across the water and cars drive on it. There are lots of pretty lights. But honestly, all the coolest cities know that you aren't really a city without a rockin' bridge. And considering this one revolutionized the commute and flow of traffic for millions of people, it is worth a look.
I've found that the best place to view the bridge is from the Odaiba side. Walk along the boardwalk back from the station and shopping area to towards the bridge. Follow the beach all the way around to the old battery, go up the stairs and turn right. You'll end up nearly under the bridge, with an excellent view of the city behind it. At night there is almost nobody in the area, so an evening picnic with your special someone won't be interrupted by throngs of other people with the same idea.
As there are many sites in Odaiba, it's only natural that you will find a spot to see the Rainbow Bride. I viewed it from the beach but was a little disappointed. With a name of "Rainbow Bridge," I was hoping for some extravagant lights of all colors or at least something resembling a rainbow. It was just a bridge though, of course a nice bridge and fine to look at, but nothing of what I had expected. However, from the beach it was possible to see the Rainbow Bridge with Tokyo Tower, and close to the Rainbow Bridge was the small copy of the Statue of Liberty and a hotel in the shape of the Coliseum. So while the Rainbow Bridge wasn't as exciting, the area around it was cool with all the copies of world famous creations.